Electrochemical measurements Cyclovoltammetry Cyclovoltammetry

Cyclovoltammetry (CV or triangle voltage method) is an analytical method for the characterization of electrochemical processes. The current that occurs at a particular voltage is measured. The three-electrode arrangement is commonly used for the measurement. The electrodes are the working electrode, reference electrode and counter electrode. The desired voltage V0 is applied between the working electrode and the reference electrode. The reference electrode must be a non-polarizable elec-trode to measure the potential. The voltage at the working elecelec-trode changes. This is where the electrochemical reactions take place. When an electrochemical reaction takes place at the working electrode, the voltage changes as electrons are withdrawn or released by the electrode. The reference electrode detects this and a current is sent from the counter electrode to the working electrode to adjust the voltage Vi to set the potential V0 again. The counter electrode is usually made of the same mate-rial as the working electrode. It is important for the reference electrode to adjust its potential quickly and remain constant. In cyclovoltammetry, a triangle voltage is applied over a certain period of time and is repeated cyclically in a certain scan rate (potential change per time).^[265] The CV of a EDLCs is described by a rectangular voltammogram with current proportional to capacitance and scan rate υ = dV/dt.^[94]

When a voltage is applied at a constant scan rate, a constant limiting current flows, which is caused by the charging of the electric double layer. Figure 28 a shows the CV of a symmetric two electrode EDLC with activated carbon as electrode material and EMImBF4 as electrolyte. At a low scan rate, the CV shows slightly rounded corners, which are caused by the internal resistance RESR. Before the capacitive cur-rent is reached, the system has to overcome the internal resistance.^[95] At higher scan rates the effects of RESR become more pronounced owing to the higher cur-rents, causing a rounding of corners after each direction switch. At the extreme, the CV will begin to resemble the diagonal line of pure resistance. Plateau capacitance

− occurring where the current has stabilized to constant value decreases with in-creased scan rate, reflecting the effects of RESR. Another deviation of the CV curve can occur, which is not related to the occurrence of any Faradaic charge transfer

59 and has become known as the butterfly-shape of CVs and is related to electrochem-ical doping as seen in Figure 28 b, which shows a symmetric carbon EDLC with TEABF4 in ACN as electrolyte in a three-electrode configuration. The term “but-terfly” describes the symmetric increase in capacitance during charge and discharge for positive and negative polarization. The lower capacitance at low potentials re-sults from the low space charge capacitance which is the capacitive component in-side the electrode material and depends on the density of states of the electrode material or charge carriers. Especially in materials with a limited number of charge carriers when separation occurs between the heavily charged surface and the de-pleted bulk material, like amorphous activated carbons, the space charge capaci-tance is the limiting factor for the overall capacicapaci-tance. It is assumed, that the charge carrier density increases with the potential, which results in an increase of capaci-tance at the vertex of the CV, and the decrease at low potentials correspond-ingly.^[14,266] Faradaic charge transfer processes will also lead to distortions of the rectangular CV shape. Redox processes that are not continuous with voltage can be revealed via CV as the curve of the investigate capacitor will show redox bumps at the respective voltage of the occurring redox process.^[267–269] This can be seen in Figure 28 c where the redox peaks are caused by the redox active surface species with 1 M H2SO4 as electrolyte. It is also possible to observe electrochemical degra-dation processes near the edge of the electrochemical stability window. As shown in Figure 28 d the current increases significantly which is due to the electrochemical degradation of the electrolyte, the electrode material, the current collector or the binder. Because these phenomena can be readily identified in the CV curves, cy-clovoltammetry is also frequently used for the qualitative analysis of EDLCs.

60

Figure 28: Common deviations from an ideal capacitor-like behavior in superca-pacitors. a) Increased scan rate or higher material resistance increases the resistive response. b) Electrochemical doping results in the butterfly-shape of CVs. C) re-dox reactions will show as rere-dox bumps at the respective voltage. d) electrochem-ical degradation of the electrolyte, current collector or the binder.^[270] Copyright 2014, Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.

Charge discharge measurements

Another method for characterizing capacitors is galvanostatic charge/discharge (CDC) measurement. The capacitor is charged to a fixed voltage with a constant current. When the voltage is reached, the capacitor is discharged with the same current. Ideal capacitors in the CDC show a linear time/voltage curve at constant current and the capacitance is calculated from the slope. At the beginning of the discharge there is an IR voltage drop as shown in Figure 29. The linearity of the "

voltage time " can be distorted by pseudocapacitance or saturation of the pores.^[271]

The apparent magnitude of the IR drop is doubled at switching during cyclic CDC experiments compared to the voltage drop at the discharge experiment from a con-stant voltage as shown in Figure 29. The voltage drop upon switching to discharge

61 is twice as large because the true capacitor voltage will lag the applied voltage dur-ing chargdur-ing owdur-ing to RESR.^[94]

Figure 29: Profile of a CDC measurement of a drop from constant voltage (left) and a CDC cycle switch (right).^[94] Copyright 2017, Spinger Berlin Heidelberg.

Electrochemical impedance spectroscopy

In the electrochemical impedance spectroscopy (EIS) a constant voltage is applied to the investigated system, which is superimposed by an alternating voltage in the order of a few millivolts. The measured variable is the current. The frequency of the alternating voltage is varied during the measurement. A typical measuring range extends over frequencies from 0.01 Hz to 1 MHz. The applied alternating voltage generates a phase-shifted alternating current. The low amplitude of the superim-posed alternating voltage ensures that the system behaves pseudo-linearly. This means that the frequencies of the alternating current and the alternating voltage are identical. The sinusoidal alternating voltage V(t) is described by equation (17) and the alternating current I(t) phase-shifted by the angle ϕ by equation (18), where ω is the angular frequency and t the time.

𝑉(𝑡) = 𝑉₀𝑠𝑖𝑛(𝜔𝑡) (17) 𝐼(𝑡) = 𝐼₀𝑠𝑖𝑛(𝜔𝑡 + 𝜙) (18)

62

With the Euler relation, it is possible to describe the alternating voltage and alter-nating current as complex units where j is the imaginary unit.

𝑉(𝑡) = 𝑉₀𝑒^𝑗𝜔𝑡 (19)

𝐼(𝑡) = 𝐼₀𝑒^{𝑗(𝜔𝑡+𝜙)} (20) The frequency-dependent, complex impedance Zw is the alternating current re-sistance and is described as the quotient of complex voltage and complex current, analogous to Ohm’s law:

𝑍(𝜔) = 𝑉(𝑡)

𝐼(𝑡) = |𝑍(𝜔)| · 𝑒^−𝑗𝜙 (21) The impedance is made up of a real part (ZRe) and an imaginary part (ZIm) and can be expressed by the following equation:

𝑍(𝜔) = 𝑍_Re+ 𝑗 · 𝑍_Im (22) In the following, ZRe will be referred to as Z’ and ZIm as Z’’. The real part of the impedance describes all processes, which lead to a real loss of energy, like Ohmic resistances. The imaginary part of the impedance describes resistive processes, which lead to a temporary energy loss, but will be restored afterwards, like capaci-tive and induccapaci-tive processes. The capacitance can be calculated from the imaginary part of the resistance by the means of the following equation:

−𝑍′′ = 1

𝜔𝐶 (23)

The data of an impedance measurement can be displayed in a complex plane as a Nyquist diagram. The real part is plotted on the abscissa and the imaginary part on the ordinate. The amount of the complex impedance − also called impedance mod-ulus − is called apparent resistance and corresponds to the vector length in the com-plex plane, and is calculated according to the Pythagorean Theorem:

|𝑍(𝜔)| = √𝑍_Re²+ 𝑍_Im² (24) The phase angle ϕ is the angle between the pointer and the real axis in the complex plane and is calculated by the following equation:

63 𝜙 = tan⁻¹(𝑍_Im

𝑍_Re) (25)

A typical Nyquist plot is shown Figure 30 a. In the high frequency part of the im-pedance, induction behavior can be observed, caused by the test cell setup and con-necting cables. The intersection of the impedance with the real impedance shows the equivalent serial resistance, which is described in section 1.4.1. It reflects the bulk resistance of the electrolyte, contact resistance of electrode material and cur-rent collector as well as intrinsic resistance of the carbon electrode. A semicircle in mid to higher frequency region up to 50 Hz, reflects the charge transfer resistance from faradaic charge transfer reactions and charge accumulation of electrolyte ions on the electrode surface.^[272] Faradaic charge transfers can be caused by impurities of carbon electrodes that lead to the decomposition of the electrolyte and narrow pores, which hinder the access of electrolyte ions on the electrode surface. In addi-tion, the Warburg resistance, a short 45° segment at mid frequencies up to 5 Hz, is related to the diffusion resistance of the electrolyte ions within the pore network.

To be more precise, surface diffusion of the adsorbed ions and diffusion within narrow pores might be responsible for the Warburg impedance.^[131] At low frequen-cies, a straight line with a large slope shows ideal double layer behavior. Whether the impedance has a straight line at low frequencies or not, can be determined with the phase angle. For perfect double layer, the phase angle is very close to −90°. The phase angle as a function of the frequency is called Bode plot and is shown in Figure 30 b. It is an illustrative representation of the results of the impedance measurement, since it represents a frequency dependence, which is often easier to interpret. Devi-ations from the ideal phase angle are mainly due to geometric aspects such as elec-trode porosity and elecelec-trode roughness, but also active site activation energy dis-persion, which causes ohmic resistances, leading to a slope of the straight line at low frequencies of the impedance in the Nyquist plot.^[95]

64

Figure 30: (a) Nyquist and (b) Bode plots for a schematic impedance model, valid for supercapacitors.^[131] Copyright 2018, Reproduced by permission of the Royal Society of Chemistry.

65